Neutral bions in the ℂ C P N −1 model

We study classical configurations in the C P N −1 model on R 1 × S 1 with twisted boundary conditions. We focus on specific configurations composed of multiple fractionalized-instantons, termed “neutral bions”, which are identified as “perturbative infrared renormalons” by Ünsal and his collaborators. For Z N twisted boundary conditions, we consider an explicit ansatz corresponding to topologically trivial configurations containing one fractionalized instanton (ν = 1/N) and one fractionalized anti-instanton (ν = −1/N) at large separations, and exhibit the attractive interaction between the instan-ton constituents and how they behave at shorter separations. We show that the bosonic interaction potential between the constituents as a function of both the separation and N is consistent with the standard separated-instanton calculus even from short to large separations, which indicates that the ansatz enables us to study bions and the related physics for a wide range of separations. We also propose different bion ansatze in a certain non- Z N twisted boundary condition corresponding to the “split” vacuum for N = 3 and its extensions for N ≥ 3. We find that the interaction potential has qualitatively the same asymptotic behavior and N -dependence as those of bions for Z N twisted boundary conditions.